Battle for Wesnoth is a hex-based TBS that's free on Windows and has a paid version on iPhone/iPad. I can't comment on the mobile version (port might be bad), but the Windows version was great when I played it 4 or 5 years ago. They have competitive multiplayer as well as singleplayer campaigns. There is actually a lot of singleplayer content since the game is open to modding (new campaigns with custom enemies, maps, units, and stories).

Singleplayer
The gameplay in singleplayer is reminiscent of Fire Emblem as you can level up and carry over units from chapter to chapter. The main difference is that the heroes aren't all pre-made. Instead, you can build as many units as you want from bases (like in Advanced Wars or Outwitters) during a mission and surviving units stay in your army as you progress from chapter to chapter. Of course, you'll probably not want to make too many fodder units as they will all take experience points and then you won't have any powerful units. When units level up, they can job advance to new classes.

Multiplayer
The multiplayer seems to be reasonably active and has an elo-based ladder. I never played the multiplayer and haven't played Wesnoth in general for many years but I believe it's basically Fire Emblem + Advance Wars. You build units from bases like in Advance Wars, but they level up and can be promoted like in Fire Emblem. I believe there are neutral creeps on maps that you can kill to level up your heroes, though I'm not sure if these maps are used in competitive ladder. Anyway, it's free, hex-based, and highly moddable so not much to lose trying it out. Personally I prefer the simplicity of Outwitters' core rules, but Wesnoth is a good game if you're looking for some variety.